Method of Small Parameter in the Problem on Forced Oscillations of a Flexible Rod of Large Rigidity

2014 ◽  
Vol 200 (1) ◽  
pp. 126-133
Author(s):  
M. M. Khrustalev
1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.


2009 ◽  
Vol 82 (3) ◽  
pp. 584-587
Author(s):  
I. M. Martynenko ◽  
M. A. Zhuravkov ◽  
V. A. Kazakevich ◽  
O. N. Sklyar

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.


Author(s):  
S. R. Rakhmanov ◽  
V. V. Povorotnii

To form a necessary geometry of a hollow billet to be rolled at a pipe rolling line, stable dynamics of the base equipment of the automatic mill working stand has a practical meaning. Among the forces, acting on its parts and elements, significant by value short-time dynamic loads are the least studied phenomena. These dynamic loads arise during transient interaction of the hollow billet, rollers, mandrel and other mill parts at the forced grip of the hollow billet. Basing of the calculation scheme and dynamic model of the mechanical system of the ТПА 350 automatic mill working stand was accomplished. A mathematical model of dynamics of the system “hollow billet (pipe) – working stand” within accepted calculation scheme and dynamic model of the mechanical system elaborated. Influence of technological load of the rolled hollow billet variation in time was accounted, as well as variation of the mechanical system mass, and rigidity of the ТПА 350 automatic mill working stand. Differential equations of oscillation movement for four-mass model of forked sub-systems of the automatic mill working stand were made up, results of their digital calculation quoted. Dynamic displacement of the stand elements in the inter-roller gap obtained, which enabled to estimate the results of amplitude and frequency characteristics of the branches of the mill rollers setting. It was defined by calculation, that the maximum amplitude of the forced oscillations of elements of the ТПА 350 automatic mill working stand within the inter-roller gap does not exceed 2 mm. It is much higher than the accepted value of adjusting parameters of the deformation center of the ТПА 350 automatic mill. A scheme of comprehensive modernization of the rollers setting in the ТПА 350 automatic mill working stand was proposed. It was shown, that increase of rigidity of rollers setting in the ТПА 350 automatic mill working stand enables to stabilize the amplitude of forced oscillations of the working stand elements within the inter-rollers gap and considerably decrease the induced nonuniform hollow billet wall thickness and increase quality of the rolled pipes at ТПА 350.


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